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APPENDIX D: Answers to Selected Exercises

Chapter 1, Section A: Basic Exercises 2. (a) and (c) 3. False 4. The distribution of a variable, the sampling distri-bution of means. and the test statistic 5. People act in accordance with others expectations. Experi ments are based on pre-experimental obser-vations, we must distinguish between samples and populations, and we must be able to deal with inconsistent data. 6. A sample is a subset of the population of interest. A popu lation is all the members of the group that we are interested in. 7. Sample; my interest is in all UNLV students. 8. Population; my interest is in this class itself. 9. (a) 19 (b) 19 (c) 58 (d) 231 10. (a) 8/36 = .22 (b) 4/36 = .11 11. (a) 1/365 = .003 (b) 31/365 = .085 (c) 28/365 = .077 (d) 52/365 = .142 (e) 53/365 = .14512. (a) 4/52 = 1/13 = .08 (b) 4/12 = 1/3 = .33 (c) 1/13 = .08 Chapter 2, Section A: Basic Exercises 2. (a) Interval/ratio (b) Ordinal (c) Nominal (d) Ordinal (e) Nominal (f) Interval/ratio 3. (a) Continuous (b) Discrete (c) Discrete (d) Continuous 4.

578 Appendix D Answers to Selected Exercises 10. Unimodal, symmetric 2 3 4 f Length of Grass (in.) – – ...

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Transcription of APPENDIX D: Answers to Selected Exercises

1 Chapter 1, Section A: Basic Exercises 2. (a) and (c) 3. False 4. The distribution of a variable, the sampling distri-bution of means. and the test statistic 5. People act in accordance with others expectations. Experi ments are based on pre-experimental obser-vations, we must distinguish between samples and populations, and we must be able to deal with inconsistent data. 6. A sample is a subset of the population of interest. A popu lation is all the members of the group that we are interested in. 7. Sample; my interest is in all UNLV students. 8. Population; my interest is in this class itself. 9. (a) 19 (b) 19 (c) 58 (d) 231 10. (a) 8/36 = .22 (b) 4/36 = .11 11. (a) 1/365 = .003 (b) 31/365 = .085 (c) 28/365 = .077 (d) 52/365 = .142 (e) 53/365 = .14512. (a) 4/52 = 1/13 = .08 (b) 4/12 = 1/3 = .33 (c) 1/13 = .08 Chapter 2, Section A: Basic Exercises 2. (a) Interval/ratio (b) Ordinal (c) Nominal (d) Ordinal (e) Nominal (f) Interval/ratio 3. (a) Continuous (b) Discrete (c) Discrete (d) Continuous 4.

2 (a) 5 (b) 7 (c) 14 (d) 188 (e) 196 (f) No (g) 84 (h) No (i) 153iXiXi2Xi + 10Xi2 51636163121111 4398119764 5255205636163160010 57 3 9 7 4 Xi = 14 (Xi + 10) = 84 Xi2 = 188 (Xi2 5) = 153 5. (a) Five (b) XiXi23Xi23Xi2 6(3Xi2 6) 3 . 6 [(3Xi2 6)/4] = 6. (a) 6 (b) XYXY326441671731133 XY = 62575 APPENDIX D: Answers to Selected Exercises Copyright 2012, Russell T. Hurlburt. Printed with permission by Kendall Hunt APPENDIX D Answers to Selected Exercises 7. (a) Seven (b) XYX Y(X Y)22(X Y)2X + Y22()XYXY ++ 86412814 [2(X Y)2/(X + Y)] = , we report [2(X Y)2/(X + Y)] = 8. (a) 83 289 (b) 37 22 (c) 353 484 (d) 62 306 9. (a) 2 (b) 10. (a) (b) (c) (d) (e) (f) (g) (h) (i) 2, Section C: Cumulative Review 18. (a) .01 (b) 0 (c) .50 (d) .50 (e) .26 (f) .09 (g) .19 (h) .09 19..10 20..02 Chapter 3, Section A: Basic Exercises 2. (a)9 8 7 6 5 4 3 2 1 0 8 11 12 15 16 19 20 23fDistance Ridden (mi.)

3 (b) Perhaps the figure with four groups is preferred because, given the small number of data points, the histogram with wider intervals makes the distribution appear smoother. 3. (a) Frequency distribution Score on First Examf96195191390189188286284283282181175 172171168161122 (b) Grouped frequency distribution Score on First Examf95 99290 94485 89580 84675 79170 74265 69160 64122 (b) (continued) With 60 as the lowest lower limit, the groups break on even numbers. which is desirable. Furthermore, the groups correspond to letter grades if one uses a 90 80 70 60 system. Those choices are made on the basis of judgment and knowledge about the data, not on purely statistical grounds, so you may have chosen a different (equally defensible) 2012, Russell T. Hurlburt. Printed with permission by Kendall Hunt 3, Section A: Basic Exercises 577 (c) Histogram6 5 4 3 2 1 0 60 64 65 69 70 74 75 79 80 84 85 89 90 94 95 99fScore on First Exam (d) Frequency polygon6 5 4 3 2 1 0 62 67 72 77 82 87 92 97fScore on First Exam 4.

4 68 74 80 86 92fHeight of Basketball Players (in.) Distribution of heights of basketball players (unimodal, slight negative skew), according to my eyeball 5. 5 6 7 8 9fVibrato Frequency (Hz) Distribution of frequencies of musicians vibrato (unimodal, symmetric, approximately normal), according to my eyeball 6. 16 17 Bottle Contents (oz) Distribution of contents of Coke bottles (unimodal, sym metric, approximately normal), according to my eyeball 7. 3 4 5 6 7fLength of McDonold s French Fries (in.) Distribution of lengths of McDonald s french fries (uni modal, slight negative skew), according to my eyeball 8. 3 4 5 6 7fLength of Royal Perfecto French Fries (in.) Distribution of lengths of Royal Perfecto french fries (uni modal, symmetric) 9. 40 50 60 70 80fHeight of Attendees (in.) Heights of attendees at Big Brothers Club luncheon (bi modal, slightly asymmetric), according to my eyeballCopyright 2012, Russell T.

5 Hurlburt. Printed with permission by Kendall Hunt APPENDIX D Answers to Selected Exercises 10. Unimodal, symmetric 2 3 4fLength of Grass (in.) 11. Distribution is shifted to the right and wider 2 3 4 5 6fLength of Grass (in.) 12. (a) Bar graph (b)5000 4000 3000 2000 1000 Lib. Sci. & Perf. Health Bus. & Educ. Arts Math. Art Sci. 3, Section C: Cumulative Review 21. (a) 1/4 (b) 1/4 (c) 1/2 (Chap. 1) 22. (a) 17 (b) 4722 (Chap. 2) 24. (a) Interval/ratio (b) Ordinal (c) Nominal (Chap. 2)Chapter 4, Section A: Basic Exercises 2. (a) 2 (b) (c) (d) Sample and population mean formulas always give iden tical results for the same data. (e) One could say either There is no mode or There are four modes ( 2, 3, 4, and 5). That illustrates a difficulty with the concept of the mode. (f) 4 3. (a) F (78 or 79 would be fine, too) (b) Equation ( ); this is a population because your interest is in only that week. (c) F (d) Estimate was close enough.

6 (e) Step 2 for an odd number of data points (f) 82 F (g) 82 F 4. (a) F (63 or 64 would be fine, too) (b) Equation ( ); this is a sample of all July days. (c) F (d) Estimate was close enough. (e) Step 3 for an even number of data points (f) F (g) 66 F 5. (a) 15 miles (b) between about 15 and 16 (c) between about 15 and 16 (d) Equation ( ); this is a sample. (e) miles (g) Step 3 for an even number of data points (h) 15 miles (i) modal interval is 14 16 (j) 15 miles 6. (a) points (78 or 79 would be fine, too) (b) between about 82 and 84 (c) between about 82 and 84 (d) Equation ( ), assuming that the question implies that we are interested only in that class (e) points (g) Step 3 for an even number of data points (h) 85 points (i) modal interval is 80 84 (j) 91 pointsCopyright 2012, Russell T. Hurlburt. Printed with permission by Kendall Hunt 4, Section C: Cumulative Review 579 (k) points (l) The lowest point (61) is only a single, unusu-ally low point (often called an outlier ).

7 This single point affects the eyeball-estimate more than it affects the computed mean. 7. Actual mean is 8. (a) 7 Hz (b) 7 Hz (c) 7 Hz 9. (a) oz (b) oz (c) oz 10. (a) in. (b) in. (c) in. (d) The mean (and to a lesser extent the median) is pulled down by the negative skew. 11. (a) in. (b) in. (c) in. 12. (a) Ordinal; mode or median (b) Nominal; mode (c) Interval/ratio; mode, median, or mean (d) Nominal; mode (e) Ordinal; mode or median (f) Interval/ratio; mode, median, or mean 13. (a) Sample (b) Population (c) SampleChapter 4, Section C: Cumulative Review 24. (a) .64 (b) .46 (c) .17 (d) .47 (e) P(Republican female) P(Republican | female) (Chap. 1)25. (a) 148 (b) 900 (c) The sum of the squares is not equal to the square of the sum. (d) 31 (Chap. 2)Chapter 5, Section A: Basic Exercises 2. (a) Smaller because the data set is narrower (b) 2 (c) .5 (d) .82 (e) Close enough (f) .667 3. (a) 9 F (b) F (c) Standard deviation of a population; these are the only days of interest; F (d) No discrepancy (e) Variance of a population; [ F]2 4.

8 (a) 11 F (b) F (c) The standard deviation of a sample; F (d) Close enough (e) Variance of a sample; [ F]2 5. (a) miles (d) Standard deviation of a sample; miles (f) Variance of a sample; miles2 6. (a) points (d) Standard deviation of a population; points (e) Close enough (f) Variance of a population; points2 7. Actual standard deviation is 8. About .6 Hz 9. About .3 ounce 10. About .7 inch 11. About .0 inchChapter 5, Section C: Cumulative Review 23. (a) Interval/ratio (b) Ordinal (c) Nominal (d) Interval/ratio (e) Nominal (Chap. 2) 24. (a) years (b) 43 years (c) years (d) years (Chaps. 4, 5) 25. (a) 27 (b) 29,079 (c) 461,041 (Chap. 2) 26. (a) 5 (b) (c) (d) (Chaps. 4, 5)Chapter 6, Section A: Basic Exercises 2. (a) 3 minutes (b) 80% (c) 100% 3. (a) .657 (b) 9 minutes 4. 34 plus large half of .14 (about .08), so about .42, or 42%; actually 5. (b) zby eyeball 2 (c) z = (e) 95% 6. zupper 5% = 2012, Russell T.

9 Hurlburt. Printed with permission by Kendall Hunt APPENDIX D Answers to Selected Exercises 7. (a) From z = 0 to z slightly greater than 2; area 34% + 14% + a wee bit, or about 48%. Actually (b) Left half area 49%; right half is 34% + large 2/3 of 14% 45%; shaded area 94%. Actually (c) Left z = .8, so left area 28%; right z = 1, so area 34%; shaded area 62%. Actually (d) A bit more than the last 2%, so area 4%. Actually 8. (a) 2 (b) 1 (c) .1 (d) 0 (e) 9. (a) 1100 hours (b) 800 hours (c) 1138 hours (d) 980 hours (e) 1000 hours 10. (a) Step 4: 2%; Step 5: Expectancy (hr) 800 900 1000 1100 1200 j = 100 hr (b) Step 4: 93%; Step 5: Life Expectancy (hr) 800 900 1000 1100 1200 j = 100 hr (c) Step 1: The figure is a combination of the fig-ures in parts (a) and (b). Step 4: 91%; Step 5: 11. (a) hours (b) 12. (a) 1 (b) Percentage of area below z = 1 is (c) z135 = , area below mean is .4479 (half-way be tween.)

10 4474 and .4484), z235 = .875, area above mean is .3092 (halfway between .3078 and .3106), percentage = 13. 14. (a) = .84, = .85, so z80 is about 1/5 (actu-ally 5/28) of the way from .84 to .85 (much closer to .84); that is, z80 = .842 (b) .841 (c) .385 15. (a) (b) (c) 16. 17. (a) .65 (b) (c) (d) 6 Chapter 6, Section C: Cumulative Review 27. (a) days (b) 9 days (c) 8 days (d) 13 days (e) days (f) days2 (Chaps. 4, 5) 28. (a) .56 (b) .28 (c) .15 (d) .27 (Chap. 1) 29. (a) .833 (b) (c) (Chap. 6)30. Positively skewed (and asymmetric) (Chap. 3) 31. (a) 0 (b) 8 (c) No. If you answered yes, you should clear up your alge bra difficulties immediately. Try the Algebra exercise in the Personal Trainer. (Chap. 2)Chapter 7, Section A: Basic Exercises 2. Queen of clubs, 3 of clubs, ace of spades, jack of clubs, 7 of clubs 3. distribution of means; shape; center; width 4. The means are all near the center of the original 2012, Russell T.


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